World Problem

[devasquez10]

The time a basketball player spends in the air is called the "hang time." The vertical leap L measured in feet is related to the hang time t measured in seconds by the equation L = 4t 2. Sam Bucketmaster, a spectacular basketball player, often displayed a leap of 3.5 feet. Find the hang time for that leap. Round your answer to the nearest hundredth of a second, if necessary.

So I know the equation is L=4t^2
L= leap
L= 3.5 ft
So, would it be 3.5=4t^2 ?
Would I divided 4 by each side first
and then i get 0.875....Or am I wrong? A little stuck here.

 

[Dr.Peterson]

That's right for the first step. You started with

4t² = 3.5​

and divided each side by 4 to get

t² = 0.875​

Now how do you find t? That is, how do you undo squaring?

 

[devasquez10]

Do I square t and square 0.875?

 

[devasquez10]

so 0.875^1/2 =0.94 rounded

 

[Dr.Peterson]

Do I square t and square 0.875?

No, but ...

so 0.875^1/2 =0.94 rounded

This is correct. The square root of 0.875 ([MATH]\sqrt{0.875}[/MATH], also written as [MATH]0.875^{\frac{1}{2}}[/MATH] or 0.875^{1/2}) is about 0.94 (to the nearest hundredth, as requested).

Keep in mind that you should always check your answer; and that it's a good idea to check what you got before rounding so much. I get 0.93541434...; 4(0.93541434)² = 3.4999999499105424, which is effectively 3.5. So you've got it.